Solve 30x^4-2 - Socratic AI (ScanMath)

Question

Factor the expression

2 (15 x^{4} - 1)

Evaluate

30 x^{4} - 2

Solution

2 (15 x^{4} - 1)

Show Solution

x_{1} = - \frac{4 3375}{15}, x_{2} = \frac{4 3375}{15}

Alternative Form

x_{1} \approx - 0.508133, x_{2} \approx 0.508133

Evaluate

30 x^{4} - 2

To find the roots of the expression,set the expression equal to 0

30 x^{4} - 2 = 0

Move the constant to the right-hand side and change its sign

30 x^{4} = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

30 x^{4} = 2

Divide both sides

\frac{30 x ^{4}}{30} = \frac{2}{30}

Divide the numbers

x^{4} = \frac{2}{30}

Cancel out the common factor 2

x^{4} = \frac{1}{15}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{1}{15}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{15}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 15}

Simplify the radical expression

\frac{1}{4 15}

Multiply by the Conjugate

\frac{4 1 5 ^{3}}{4 15 \times 4 1 5 ^{3}}

Simplify

\frac{4 3375}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

415 \times 4 1 5^{3}

The product of roots with the same index is equal to the root of the product

4 15 \times 1 5^{3}

Calculate the product

4 1 5^{4}

Reduce the index of the radical and exponent with 4

15

\frac{4 3375}{15}

x = \pm \frac{4 3375}{15}

Separate the equation into 2 possible cases

x = \frac{4 3375}{15} x = - \frac{4 3375}{15}

Solution

x_{1} = - \frac{4 3375}{15}, x_{2} = \frac{4 3375}{15}

Alternative Form

x_{1} \approx - 0.508133, x_{2} \approx 0.508133

Show Solution